{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Augmentation Strategies "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this notebook we explore different augmentation strategies for neural differential equations. This time, we'll make use of the 3D `concentric spheres` dataset."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import sys\n",
    "sys.path.append('../')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "from torchdyn.models import *; from torchdyn.datasets import *\n",
    "from torchdyn import *"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Data**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Generate 3D nested spheres data\n",
    "d = ToyDataset()\n",
    "X, yn = d.generate(n_samples=2 << 12, dataset_type='spheres')   "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "from mpl_toolkits.mplot3d import Axes3D\n",
    "\n",
    "c = ['blue', 'orange']\n",
    "fig = plt.figure(figsize=(6,6))\n",
    "ax = fig.add_subplot(111, projection='3d')\n",
    "for i in range(2):\n",
    "    ax.scatter(X[yn==i,0], X[yn==i,1], X[yn==i,2], s=5, alpha=0.5, c=c[i])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "import torch\n",
    "import torch.utils.data as data\n",
    "device = torch.device(\"cuda:0\" if torch.cuda.is_available() else \"cpu\")\n",
    "\n",
    "# Load data into dataloader\n",
    "bs = len(X)\n",
    "X_train = torch.Tensor(X).to(device)\n",
    "y_train = torch.LongTensor(yn.long()).to(device)\n",
    "train = data.TensorDataset(X_train, y_train)\n",
    "trainloader = data.DataLoader(train, batch_size=bs, shuffle=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Learner**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "import torch.nn as nn\n",
    "import pytorch_lightning as pl\n",
    "\n",
    "class Learner(pl.LightningModule):\n",
    "    def __init__(self, model:nn.Module):\n",
    "        super().__init__()\n",
    "        self.model = model\n",
    "    \n",
    "    def forward(self, x):\n",
    "        return self.model(x)\n",
    "    \n",
    "    def training_step(self, batch, batch_idx):\n",
    "        x, y = batch      \n",
    "        y_hat = self.model(x)   \n",
    "        loss = nn.CrossEntropyLoss()(y_hat, y)\n",
    "        logs = {'train_loss': loss}\n",
    "        return {'loss': loss, 'log': logs}   \n",
    "    \n",
    "    def configure_optimizers(self):\n",
    "        return torch.optim.Adam(self.model.parameters(), lr=0.01)\n",
    "\n",
    "    def train_dataloader(self):\n",
    "        return trainloader"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Neural ODE (0-augmentation)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The first model under consideration involves 0-augmentation (often referred to as [ANODE](https://arxiv.org/abs/1904.01681)) and consisting in augmenting the state $h$ with additional dimensions $a$ which are initialized to 0 \n",
    "\n",
    "$$\n",
    "    \\left\\{\n",
    "    \\begin{aligned}\n",
    "        \\begin{bmatrix}\n",
    "            \\dot z(s)\\\\\n",
    "            \\dot a(s)\n",
    "        \\end{bmatrix} &= f([z(s), a(s)], \\theta)\\\\\n",
    "        \\begin{bmatrix}\n",
    "            \\dot h(0)\\\\\n",
    "            \\dot a(0)\n",
    "        \\end{bmatrix} &= \\begin{bmatrix}\n",
    "            x\\\\\n",
    "            0\n",
    "        \\end{bmatrix}\\\\\n",
    "        \\hat y &= Linear([z(1),a(1)])\n",
    "    \\end{aligned}\\right.\n",
    "$$\n",
    "\n",
    "With `torchdyn`, turning a neural ODE into an ANODE is as simple as using the `Augmenter` class as follows:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "# We consider 5 augmenting dimensions, i.e. the DEFunc must accomodate 8 inputs\n",
    "func = nn.Sequential(nn.Linear(8, 64),\n",
    "                            nn.Tanh(),\n",
    "                            nn.Linear(64, 8)\n",
    "                    )\n",
    "                            \n",
    "\n",
    "# Define NeuralDE\n",
    "neuralDE = NeuralDE(func, solver='dopri5').to(device)\n",
    "\n",
    "# Here we specify to the \"Augmenter\" the 5 extra dims. For 0-augmentation, we do not need to pass additional arg.s \n",
    "model = nn.Sequential(Augmenter(augment_dims=5),\n",
    "                      neuralDE,\n",
    "                      nn.Linear(8, 2)).to(device)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note that `Augmenter` can be fully-specified outside the neuralDE model. This makes it straightforward to switch between augmented and non-augmented at will."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "GPU available: True, used: False\n",
      "TPU available: False, using: 0 TPU cores\n",
      "\n",
      "  | Name  | Type       | Params\n",
      "-------------------------------------\n",
      "0 | model | Sequential | 1 K   \n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "9c0df0d11595427cba0c8b3bd8096c54",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "HBox(children=(FloatProgress(value=1.0, bar_style='info', description='Training', layout=Layout(flex='2'), max…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "1"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Train the model\n",
    "learn = Learner(model)\n",
    "trainer = pl.Trainer(max_epochs=200)\n",
    "trainer.fit(learn)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Plots**\n",
    "\n",
    "We plot models outputs $\\hat y$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 216x216 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Evaluate outputs\n",
    "y_hat = model(X_train).detach().cpu()\n",
    "\n",
    "# Plot results\n",
    "c = ['blue', 'orange']\n",
    "fig = plt.figure(figsize=(3,3))\n",
    "ax = fig.add_subplot(111)\n",
    "for i in range(2):\n",
    "    ax.scatter(y_hat[yn==i,0], y_hat[yn==i,1], s=2, alpha=0.2, c=c[i])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Neural ODE (Input-Layer (IL)-Augmentation) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Input layer augmentation ([IL-augmentation](https://arxiv.org/abs/2002.08071)) is also easy to implement with `torchdyn`. \n",
    "\n",
    "$$\n",
    "    \\left\\{\n",
    "    \\begin{aligned}\n",
    "        \\begin{bmatrix}\n",
    "            \\dot z(s)\\\\\n",
    "            \\dot a(s)\n",
    "        \\end{bmatrix} &= f([h(s), a(s)], \\theta)\\\\\n",
    "        \\begin{bmatrix}\n",
    "            \\dot z(0)\\\\\n",
    "            \\dot a(0)\n",
    "        \\end{bmatrix} &= \\begin{bmatrix}\n",
    "            x\\\\\n",
    "            g(x, \\omega)\n",
    "        \\end{bmatrix}\\\\\n",
    "        \\hat y &= Linear([h(1),a(1)])\n",
    "    \\end{aligned}\\right.\n",
    "$$\n",
    "\n",
    "where $g(x, \\omega)$ is a neural network, usually a single linear layer.\n",
    "The following is an example of a partial IL-augmentation where a linear layer is trained to determine the initial condition of the additional `5` dimensions. Notice how the `DEFunc` goes from `8` to `8` dimensions. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "# We consider 5 augmenting dimensions, i.e. the DEFunc must accomodate 8 inputs\n",
    "func = nn.Sequential(nn.Linear(8,64),\n",
    "                            nn.Tanh(),\n",
    "                            nn.Linear(64,8))\n",
    "                            \n",
    "\n",
    "# Define NeuralDE\n",
    "neuralDE = NeuralDE(func, solver='dopri5').to(device)\n",
    "\n",
    "# Here we just need to specify to the \"Augmenter\" the input layer. In this case an nn.Linear(3, 5)\n",
    "model = nn.Sequential(Augmenter(augment_func=nn.Linear(3, 5)),\n",
    "                      neuralDE,\n",
    "                      nn.Linear(8,2)).to(device)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "GPU available: True, used: False\n",
      "TPU available: False, using: 0 TPU cores\n",
      "\n",
      "  | Name  | Type       | Params\n",
      "-------------------------------------\n",
      "0 | model | Sequential | 1 K   \n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "e49e2cfae5d242d1ba52e3f5f4ded7d3",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "HBox(children=(FloatProgress(value=1.0, bar_style='info', description='Training', layout=Layout(flex='2'), max…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "1"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Train the model\n",
    "learn = Learner(model)\n",
    "trainer = pl.Trainer(max_epochs=200)\n",
    "trainer.fit(learn)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Plots**\n",
    "\n",
    "We plot models outputs $\\hat y$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 216x216 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Evaluate outputs\n",
    "y_hat = model(X_train).detach().cpu()\n",
    "\n",
    "# Plot results\n",
    "c = ['blue', 'orange']\n",
    "fig = plt.figure(figsize=(3,3))\n",
    "ax = fig.add_subplot(111)\n",
    "for i in range(2):\n",
    "    ax.scatter(y_hat[yn==i,0], y_hat[yn==i,1], s=2, alpha=0.2, c=c[i])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Note** that for a full `IL-augmentation`, the following model definition can replace the above. \n",
    "\n",
    "$$\n",
    "    \\left\\{\n",
    "    \\begin{aligned}\n",
    "        \\begin{bmatrix}\n",
    "            \\dot z(s)\\\\\n",
    "            \\dot a(s)\n",
    "        \\end{bmatrix} &= f([z(s), a(s)], \\theta)\\\\\n",
    "        \\begin{bmatrix}\n",
    "            \\dot z(0)\\\\\n",
    "            \\dot a(0)\n",
    "        \\end{bmatrix} &= g(x, \\omega)\\\\\n",
    "        \\hat y &= Linear([z(1),a(1)])\n",
    "    \\end{aligned}\\right.\n",
    "$$\n",
    "\n",
    "Determining the entire initial condition with a linear layer $g$ can be achieved without `Augmenter` as follows"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "func = DEFunc(nn.Sequential(nn.Linear(8, 64),\n",
    "                            nn.Tanh(),\n",
    "                            nn.Linear(64, 8))\n",
    "                            )\n",
    "\n",
    "neuralDE = NeuralDE(func).to(device)\n",
    "\n",
    "model = nn.Sequential(nn.Linear(3, 8),\n",
    "                      neuralDE,\n",
    "                      nn.Linear(8, 2)).to(device)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Neural ODE (Higher-Order Augmentation)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally, we take a look at increasing the order of the ODE as a method to augment the dimensions, e.g. a 2nd order neural ODE\n",
    "\n",
    "$$\n",
    "    \\left\\{\n",
    "    \\begin{aligned}\n",
    "        \\begin{bmatrix}\n",
    "            \\dot z(s)\\\\\n",
    "            \\dot a(s)\n",
    "        \\end{bmatrix} &= \\begin{bmatrix}\n",
    "           a(s)\\\\\n",
    "           f([z(s),a(s)],\\theta)\n",
    "        \\end{bmatrix}\\\\\n",
    "        \\begin{bmatrix}\n",
    "            \\dot z(0)\\\\\n",
    "            \\dot a(0)\n",
    "        \\end{bmatrix} &= g(x, \\omega)\\\\\n",
    "        \\hat y &= Linear([z(1),a(1)])\n",
    "    \\end{aligned}\\right.\n",
    "$$\n",
    "\n",
    "In `torchdyn`, the `DEFunc` can be specified to evolve according to higher orders by passing `func_type='higher_order` and `order=n` as arguments. `Augmenter` is still used to augment with `data dimension * n` additional dimensions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "func = nn.Sequential(nn.Linear(6, 64),\n",
    "                     nn.Tanh(),\n",
    "                     nn.Linear(64, 3))\n",
    "\n",
    "neuralDE = NeuralDE(func, solver='dopri5', order=2).to(device)\n",
    "\n",
    "model = nn.Sequential(Augmenter(augment_dims=3),\n",
    "                      neuralDE,\n",
    "                      nn.Linear(6,2)).to(device)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "GPU available: True, used: False\n",
      "TPU available: False, using: 0 TPU cores\n",
      "\n",
      "  | Name  | Type       | Params\n",
      "-------------------------------------\n",
      "0 | model | Sequential | 657   \n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "1242d941ef374f999250fe4a41fc7971",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "HBox(children=(FloatProgress(value=1.0, bar_style='info', description='Training', layout=Layout(flex='2'), max…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "1"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "learn = Learner(model)\n",
    "trainer = pl.Trainer(max_epochs=300)\n",
    "trainer.fit(learn)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Plots**\n",
    "\n",
    "We plot models outputs $\\hat y$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 216x216 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Evaluate outputs\n",
    "y_hat = model(X_train).detach().cpu()\n",
    "\n",
    "# Plot results\n",
    "c = ['blue', 'orange']\n",
    "fig = plt.figure(figsize=(3,3))\n",
    "ax = fig.add_subplot(111)\n",
    "for i in range(2):\n",
    "    ax.scatter(y_hat[yn==i,0], y_hat[yn==i,1], s=2, alpha=0.2, c=c[i])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "py37",
   "language": "python",
   "name": "py37"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.7"
  },
  "latex_envs": {
   "LaTeX_envs_menu_present": true,
   "autoclose": false,
   "autocomplete": true,
   "bibliofile": "biblio.bib",
   "cite_by": "apalike",
   "current_citInitial": 1,
   "eqLabelWithNumbers": true,
   "eqNumInitial": 1,
   "hotkeys": {
    "equation": "Ctrl-E",
    "itemize": "Ctrl-I"
   },
   "labels_anchors": false,
   "latex_user_defs": false,
   "report_style_numbering": false,
   "user_envs_cfg": false
  },
  "varInspector": {
   "cols": {
    "lenName": 16,
    "lenType": 16,
    "lenVar": 40
   },
   "kernels_config": {
    "python": {
     "delete_cmd_postfix": "",
     "delete_cmd_prefix": "del ",
     "library": "var_list.py",
     "varRefreshCmd": "print(var_dic_list())"
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     "delete_cmd_postfix": ") ",
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   },
   "types_to_exclude": [
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   "window_display": false
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 "nbformat": 4,
 "nbformat_minor": 4
}
